There's a hadith in Jami' at-Tirmidhi saying:
'Ikrimah, the freed slave of Ibn 'Abbas, narrated that:
Ibn 'Abbas said: “We were with the Messenger of Allah (ﷺ) when 'Ali bin Abi Talib came to him, and he said: "May my father and mother be ransomed for you! This Qur’an has suddenly left my heart, and I do not find myself capable of it."
So the Messenger of Allah (ﷺ) said to him: ‘O Abul-Hasan! Should I not teach you words that Allah shall benefit you with, and benefit whomever you teach, and they will make whatever you have learned in your chest firm?’ He said: ‘Of course, O Messenger of Allah (ﷺ), so teach me.’
He (ﷺ) said: ‘When it is the night of (before) Friday, then if you are able to stand in the last third of the night, then verily it is a witnessed hour, and supplication is answered in it. And my brother Ya'qub (as) did say to his sons: I shall seek forgiveness for you from my Lord. He said: “Until the night of Friday comes.” So if you are not able, then stand in the middle of it, and if you are not able then stand in the first of it.
And pray four Rak'ah. Recite Fatihatul-Kitab (the Opening of the Book) and Surat Ya-Sin in the first Rak'ah, and Fatihatul-Kitab and Ha-Mim Ad-Dukhan in the second Rak'ah, and Fatihatul-Kitab and Alif Lam Mim Tanzil As-Sajdah in the third Rak'ah, and Fatihatul-Kitab and Tabarak Al-Mufassal in the fourth Rak'ah. So when you have finished with the Tasha-hud, then praise Allah and mention Allah’s greatness in an excellent manner, and send Salat upon me - and be excellent in it - and upon the rest of the Prophets. And seek forgiveness for the believing men and the believing women, and for your brothers who have preceded you in faith. Then say in the end of that: “O Allah, have mercy on me by abandonment of sins forever, so long as You keep me remaining. And have mercy on me from taking upon myself what does not concern me, and provide me good sight for what will make You pleased with me. O Allah, Originator of the heavens and the earth, Possessor of glory, and generosity, and honor that is not exceeded. I ask you, O Allah, O Rahman, by Your glory and the light of Your Face, to make my heart constant in remembering Your Book as You taught me, and grant me that I recite it in the manner that will make You pleased with me. O Allah, Originator of the heavens and the earth, Possessor of glory, and generosity, and honor that is not exceeded. I ask you, O Allah, O Rahman, by Your glory and the light of Your Face, to enlighten my sight with Your Book, and make my tongue free with it, and to relieve my heart with it, and to expand my chest with it, and to wash my body with it. For indeed, none aids me upon the truth other than You, and none gives it except You, and there is no might or power except by Allah, the High, the Magnificent.
(Allāhummarḥamnī bitarkil-ma'āṣī abadan mā abqaitanī, warḥamnī an atakallafa mā lā ya'nīnī, warzuqnī ḥusnan-naẓari fī mā yurḍīka 'annī. Allāhumma badī'as-samāwāti wal-arḍi dhal-jalāli wal-ikrāmi wal-'izzatil-latī lā turāmu, as’aluka yā Allāhu yā Raḥmānu bi-jalālika wa nūri wajhika, an tulzima qalbī ḥifẓa kitābika kamā 'allamtanī, warzuqnī an atluwahū 'alan-naḥwil-ladhī yurḍīka'annī. Allāhumma badī'as-samāwāti wal arḍi dhal-jalāli wal-ikrāmi wal 'izzati-llatī lā turāmu, as’aluka yā Allāhu, yā Raḥmānu bi-jalālika wa nūri wajhika, an tunawwira bi-kitābika baṣarī, wa an tuṭliqa bihī lisānī, wa an tufarrija bihī 'an qalbī, wa an tashraḥa bihī ṣadrī, wa an taghsila bihī badanī, fa innahu lā yu'īnunī 'alal-ḥaqqi ghairuka wa lā yu’tīhi illā anta wa lā ḥawla wa lā quwwata illā billāhil-'Aliyyil-'Aẓīm).”
O Abul-Hasan! So do this three Fridays, or five, or seven, you will be answered - by the will of Allah - by the One Who sent me with the Truth, it has not failed a believer once.’”
'Abdullah bin 'Abbas said: “So, by Allah, 'Ali did not wait but five or seven until ['Ali] came to the Messenger of Allah (ﷺ) in a gathering similar to that and said: ‘O Messenger of Allah (ﷺ), indeed I was [a man] in the time that passed, who used to not take except four Ayat or about that much, so when I would recite them to myself they would suddenly depart from me, and today I learn forty Ayat or about that much, and when I recite them to myself, then it is as if the Book of Allah is before my eyes. I used to hear a Hadith and when I would repeat it, it would suddenly depart from me, and today I hear Ahadith, and when I report them, I do not err in a single letter.’ So the Messenger of Allah (ﷺ) said at that point: ‘A believer, by the Lord of the Ka`bah, O Abul-Hasan.’”
(Jami' at-Timidhi, qualified as da'if)
This hadith was also compiled by al-Hakim from Nishapure in his al-Mustadrak (see here in Arabic) -with the commentary that it is according the conditions of both al-Bukhari and Muslim- and at-Tabarani in his al-Mo'jam al-Kabeeer (see here in Arabic)
As for the narrator chain of imam at-Tabarani it has many flaws and therefore this narration can't be taken as more than da'if, while the chain of al-Mustadrak and at-Tirmidhi (and apparently also chosen by a-Darimi) is a sound one imam a-Dhahabi said (in his commentary of al-Mustardak: Talkheess al-Mustadrak تلخيص المستدرك):
هذا حديث منكر شاذ ، أخاف لا يكون موضوعا ، وقد حيرني والله جودة سنده
This hadith is strongly rejected and shaadh, I'm afraid it is a fabrication, and by Allah it caused me some trouble due to the quality of the narrator chain.
He comes to the conclusion that the narrator chain is rather good, but the content is very strange.
Most scholars say it is a fabrication and rejected and consider Al-Walid ibn Maslamah الوليد بن مسلم the issue in the chain as he used to make tadless at-Taaswiyah (What exactly is tadlees?), a-Dhahabi in his siyar 'alaam an-Nubala' when quoting him quoted this hadith as the most rejected narration of him see here in Arabic. Commenting it after fully quoting the narration by saying: and I consider this hadith as a fabrication.
As-Sakhawi added a less weighty argument by saying that ibn Juraij here has narrated from 'Ata' (which actually is confirmed by a-Dhahabi in his siyar 'alaam an-Nubala' and shouldn't be the correct issue) both versions appear in ibn Jawzi's (Al-Mawdo'at لموضوعات).
This fatwa on islamqa #139768 -in Arabic- says due to the strong rejection of this hadith and the fact that it is rather a fabrication one shouldn't take it seriously and follow it.
Note that one might perform or apply a weak hadith in some cases, but not a fabricated one. Therefore it is considered bid'ah in this fatwa on islamweb #344.
While this fatwa #2237 on islamonline says the hadith didn't reach the degree of soundness and what it includes is a (nafl) prayer, a Qur'an recitation, dhikhr and du'a which all basically are allowed, but the result is in the hand of Allah as even if it applied for 'Ali it might not be the same for others. And worship is a good deed and it's desired and its is also hoped for to be accepeted beside the du'a.